Initial state effects on the cosmic microwave background and trans-Planckian physics

There exists a one complex parameter family of de Sitter invariant vacua, known as α vacua. In the context of slow roll inflation, we show that all but the Bunch-Davies vacuum generates unacceptable production of high energy particles at the end of inflation. As a simple model for the effects of trans-Planckian physics, we go on to consider non–de Sitter invariant vacua obtained by patching modes in the Bunch-Davies vacuum above some momentum scale M_c, with modes in an α vacuum below M_c. Choosing M_c near the Planck scale M_Pl, we find acceptable levels of hard particle production, and corrections to the cosmic microwave perturbations at the level of HM_Pl/M_c², where H is the Hubble parameter during inflation. More general initial states of this type with H≪M_c≪M_Pl can give corrections to the spectrum of cosmic microwave background perturbations at order 1. The parameter characterizing the α vacuum during inflation is a new cosmological observable.